The versatility of using rational functions as approximants is shown to facilitate the residue-approximation method for calculating mean extinctions in a wide range of applications. We address the problem of approximating or representing a number of practical particle-size distributions with use of rational functions. The accuracy of the residue-approximation method is examined by several kinds of size distribution as well as for different types of particles. Clearly our residue-approximation method is both efficient and accurate for most applications.